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Byju's Answer

Standard XII

Physics

Matter Waves

The relation ...

Question

The relation between the intensity ( $I$ ) of a wave and the distance ( $r$ ) from a line source is

I \propto r^{- 1}

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I \propto r^{- 2}

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I \propto r

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I \propto r^{- 1 / 2}

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Solution

The correct option is A $I \propto r^{- 1}$
For a line source intensity, $I = \frac{p}{A} = \frac{p}{(2 π r)} ν$

$∴ I \propto \frac{1}{r}$ , hence the correct answer is A.

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Similar questions

Q. Match the following columns. Here,

I

represent intensity,

A

amplitude and

r

distance from the source.

Column $I$	Column $II$
$a .$ $I$ due to point source	$p .$ $\propto r^{- 1 / 2}$
$b .$ $A$ due to point source	$q .$ $\propto r^{- 1}$
$c .$ $I$ due to line source	$r .$ $\propto r^{- 2}$
$d .$ $A$ due to line source	$s .$ $\propto r^{- 4}$

Q. Match the following columns. Here,

I

represent intensity,

A

amplitude and

r

distance from the source.
Column

I

Column

II

a .

I

due to point source

p .

\propto r^{- 1 / 2}

b .

A

due to point source

q .

\propto r^{- 1}

c .

I

due to line source

r .

\propto r^{- 2}

d .

A

due to line source

s .

\propto r^{- 4}

Q. At distance

r

from a point source with power

P_{a v}

, the wave intensity is

I = P_{a v} / 4 π r^{2}

. prove that a point source with power

P_{a v}

moving with constant speed

v_{S}

. the wave intensity is

I = \frac{P_{a v}}{4 π r^{2}} (\frac{v - v_{S}}{v})

Consider the earlier problem where we had a point source radiating energy at the rate of 10 Joules per second, or 10 Watts. What can you say about the intensities $I_{1} a n d I_{2}$ at two points on spheres of radii and $r_{1} a n d r_{2}$ respectively, centered at the source?

Q. A travelling wave is partly reflected and partly transmitted from a rigid boundary. Let

a_{i}, a_{r}

and

a_{t}

be the amplitudes of incident wave, reflected wave and transmitted wave and

I_{i}, I_{r}

and

I_{t}

be the corresponding intensities. Then, choose the correct alternative.

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The relation between the intensity (I) of a wave and the distance (r) from a line source is

The correct option is A I∝r−1For a line source intensity, I=pA=p(2πr)ν∴I∝1r , hence the correct answer is A.

The relation between the intensity ( $I$ ) of a wave and the distance ( $r$ ) from a line source is

The correct option is A $I \propto r^{- 1}$
For a line source intensity, $I = \frac{p}{A} = \frac{p}{(2 π r)} ν$

$∴ I \propto \frac{1}{r}$ , hence the correct answer is A.